Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices

DOI10.1007/s00220-016-2739-zzbMath1352.37163arXiv1504.03448OpenAlexW2230036372MaRDI QIDQ330891

Thomas Lam, Pavlo Pylyavskyy, Rei Inoue

Publication date: 26 October 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03448

zbMATH Keywords

Toda lattice\(R\)-matrixspectral mapJacobian of the spectral maptoric network

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12) Jacobians, Prym varieties (14H40) Relationships between algebraic curves and integrable systems (14H70) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices, Discrete dynamics in cluster integrable systems from geometric \(R\)-matrix transformations, Invariants of Weyl group action and \(q\)-characters of quantum affine algebras, Cluster Toda chains and Nekrasov functions, Soliton cellular automata associated with infinite reduced words

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable cluster dynamics of directed networks and pentagram maps
• Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices
• Total positivity in loop groups. I: Whirls and curls
• Perfect matchings and the octahedron recurrence
• The spectrum of difference operators and algebraic curves
• Promotion des morphismes d'ensembles ordonnes
• Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry
• Theta functions on Riemann surfaces
• Crystals and total positivity on orientable surfaces
• A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice
• Affine geometric crystals in unipotent loop groups
• Inverse Problem in Cylindrical Electrical Networks
• Path description of conserved quantities of generalized periodic box-ball systems
• Tropical R maps and affine geometric crystals
• Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Affine geometric crystals and limit of perfect crystals
• Tropical Spectral Curves and Integrable Cellular Automata
• Solution of the generalized periodic discrete Toda equation II: theta function solution
• AFFINE CRYSTALS AND VERTEX MODELS
• Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang-Baxter Equation
• Dimers and cluster integrable systems
• Solutions of the generalized periodic discrete Toda equation
• A note on quantum groups and relativistic Toda theory